On Equitorsion Geodesic Mappings of General Affine Connection Spaces

Abstract

In the papers [19], [20] several Ricci type identities are obtained by using non-symmetric affine connection. In these identities appear 12 curvature tensors, 5 of which being independent [21], while the rest can be expressed as linear combinations of the others. In the general case of a geodesic mapping f of two non-symmetric affine connection spaces GAN and GAN it is impossible to obtain a generalization of the Weyl projective curvature tensor. In the present paper we study the case when GAN and GAN have the same torsion in corresponding points. Such a mapping we name ”equitorsion mapping”. With respect to each of mentioned above curvature tensors we have obtained quantities E θ i jmn (θ = 1, · · · , 5), that are generalizations of the Weyl tensor, i.e. they are invariants based on f . Among E θ only E 5 is a tensor. All these quantities are interesting in constructions of new mathematical and physical structures. AMS Subj. Class.: 53B05.